# History of Mathematics

Historyof Mathematics

Historyof mathematics primarily focuses on the investigation of the originof some of the discoveries in mathematics. The study also focuses onmethods of mathematics and notation in the past. Previously, therewas no global spread of information, written illustrations and nodevelopments in mathematics (Boyer, Carl and Merzbach, 6). However,this has come into existence in modern days. The most ancient textsof mathematics available are mathematical papyrus that is Egyptianmathematics 2000-1800 BC, the Babylon mathematics 1900 BC and Moscowpapyrus mathematics 1890 BC. All of the above texts were concernedwith Pythagoras theorem that is thought to be the earliest andextensive development of mathematics after the geometry andarithmetic’s (Boyer, Carl and Merzbach, 6).

Thestudy of mathematics history is a unit on its own which began in thecentury of 6^{th}BC through the introduction of Pythagoreans. They devised the namemaths from Greek mathema which means the unit or subject ofinstruction. The mathematics of Greek greatly refined some methodsthat are through the introduction of mathematical evidence anddeductive reasoning, and then expanded mathematics as a subject(Bunt, et al., 117).On the same note, the mathematics of Chinese made some initialcontributions, which include place value system. There was anevolution of Hindu-Arabic numerical system and instructions to enablethe use of its operation in the whole world of millennium, and thesewere transmitted to Islamic mathematics west through Muhammad’swork. In turn, the math’s expanded to theses civilizations. ManyArabic and Greek were totally translated to Latin. This led toadvance improvements in medieval Europe (Bunt, et al., 117).

Pre-Historic

Theoriginality of mathematics lies in the theories of magnitude andnumber form. Modern research on animal reasoning has revealed thatthose conceptions are not exceptional to a human being. The idea ofnumbers have evolved gradually over the last decades this has beensupported by how the language exist which in long run preserved thedifference between one and two but not larger than two. Prehistoricwas discovered in Africa 20000 years ago. However, others argue thatit may be more than 20000 years(Bunt, et al., 117).

BabylonianTreatment of Quadric Equations

Babylonianmathematics of quadric equations refers to mathematics that belongsto peoples of Mesopotamia. That is from early days of Sumerianthrough Hellenistic period that is drawn to Christianity. The name ofBabylonian mathematics was because of the fundamental part played byBabylonian as a study place. Later it went to Arab, Mesopotamia andempire, especially Baghdad became an important center study ofIslamic mathematics (Friberg,279).The region of Babylonian had been the center of Sumerian civilizationthat succeeded before 3500 BC. This advanced civilization issupporting people, the legal system, and administration. There wasthe development of writing and counting that was based on sexagesimalsystem meaning base 60. The backward culture of Akkadians invadedthe area around 2300 BC and mixed up with some advanced culture ofSumerians. The Akkadians later invented the abacus to be used as aninstrument for calculating, and somehow they developed some awkwardmethods of arithmetic with subtraction, addition, division andmultiplication playing a significant part. The Sumerian, on the otherhand, appalled against the rule of Akkadian and by 2100 BC, there wasno option, so they went back to school(Friberg, 280).

Thecivilization of Babylonia whose mathematics is the topic of articlereplaced the Sumerians after two thousand BC. The Babylonian wasconsidered to be Semitic people that invaded Mesopotamia defeatingSumerians and around 1900BC they developed their resources at theBabylon. Moreover, the Sumerians had established an immaterial methodof writing that was based on cuneiform, which is a slice molded sign.Their signs were transcribed on the tablet of wet clay soil which wasparched in the warm sun (Friberg,282).These tablets are still used recently. This was the usage of styluseson the medium clay tablet that directed it to the usage of symbols ofcuneiform because it was not easy to draw curved lines. Then laterBabylonian accepted the same cuneiform style of writing on soiltablets.

Mostof the tablets concerned the topics that though were not containingdeep mathematics but were fascinating, for instance, the mention ofthe irrigation system of early civilization in Mesopotamia (Friberg,286). The Babylonians had advanced number system in fact it was moreadvanced than the modern ones. It was a system of position with base60 on the contrary of the system with the base of 10 which iswidespread and is used today. The Babylonians made a division of thedaytime and night into hours of 24, every one hour divided into sixtyminutes, and then every one minute divided into exact sixty seconds.This system of calculating survived for about 4000 years. That is totranscribe 5h25m 30s means 5 hours, there are 25 minutes and 30 seconds, and it isjust like to write a sexagesimal fraction, 5 5/12 1/120. Hence,there is the adoption of notation for 5 25, 30 for the sexagesimalnumber. As the base ten portions the number of sexagesimals is 5 ^{4/102/100 }5/1000is written in decimal form as 5.425 (Friberg,279).

Themost remarkable characteristic of Babylonian’s computing abilitieswas their creation of tables to help the calculation. The two tabletsfound at Senkerah on the date of 1854 as from 2000 BC. They providethe squaring of digits up to fifty-nine and cubes of digits tothirty-two. The table gives eight^{2} =1, four which stands for eight^{2} =1, four = 1 × sixty + four = 64

Thiscontinues up to fifty nine^{2} =58, 1 (= fifty eight× 60 + one = 3481).

TheFormula used by the Babylonians

ab ={(a + b)^{2} - a^{2} - b^{2}}/2

Tosimplify the multiplication and make it easier, the formula becomes.

*ab* ={(*a* + *b*)^{2} -(*a* - *b*)^{2}}/4

TheEgyptian Mathematics

TheEgyptian mathematical refers to mathematics that is transcribed inthe language of Egyptian. Greek replaced Egyptian as the languagewritten by the scholars of Egypt. The study of mathematics later inEgypt continued under Arab empire as the section of Arab empire whenthe Arabic became a language of Egyptian scholars (Imhausen,19).The most extensive mathematics of Egypt text is Rhind papyrus at somepoint it also called Ahmes papyrus being named after its writer. Thisis an instructional manual for the students in geometry andarithmetic. In the addition to giving areas methods of division,multiplication and operating with a unit of fractions it alsocontains the proof of other knowledge of mathematics. This includesharmonic means geometric and arithmetic and some simple understandingof both sifters of Eratosthenes and theory of perfect number.Similarly, it shows how to solve linear equations geometric seriesand arithmetic (Imhausen,21).

Anotherimportance of Egyptian mathematical text is that of Moscow papyruswhich comes from middle kingdom period dated 1890 BC. Notably, itcontains story problems and word problems which have the main purposeof entertainment (Imhausen,19).One problem is very important as it provides a technique forcalculating the capacity of the frustum. For example truncatedpyramid of 6 with vertical height by four on the base by two on theupper, there is a requisite to 4 which equals to 16. Double fourwhich equals to 8, then square 2, which equals to 4. When all areadded the result is 28. Then take 1/3 of 6 result equals to 2.Finally, take 28 twice, the result is 56 (Imhausen,19).

TheEgyptian Mathematics Formulae

WorksCited

Boyer,Carl B., and Uta C. Merzbach. *Ahistory of mathematics*.John Wiley & Sons, 2011.

Bunt,Lucas NH, Phillip S. Jones, and Jack D. Bedient. *Thehistorical roots of elementary mathematics*.Courier Corporation, 2012.

Friberg,Jöran. "Methods and traditions of Babylonian mathematics:Plimpton 322, Pythagorean triples, and the Babylonian triangleparameter equations."*HistoriaMathematica* 8.3(1981): 277-318.

Imhausen,Annette. "Ancient Egyptian mathematics: New perspectives on oldsources." *TheMathematical Intelligencer* 28.1(2006): 19-27.